The grass is wet if either it rained or the sprinkler was
on. (Create propositional symbols, and give their definitions.)

Task 3 (25 pts)

We have a knowledge base that contains:

a. \((R \rightarrow S) \wedge Q\)

b. \((J \wedge Q) \rightarrow P\)

c. \(Q \rightarrow Z\)

d. \(P \rightarrow \neg Q\)

e. \((R \rightarrow S) \rightarrow (\neg H \rightarrow J)\)

f. \((\neg Q \vee T) \rightarrow J\)

Derive each of the following using inference rules for propositional
logic. Indicate the rule used (i.e., MP for modus ponens) and the
propositions used with the rule. You can use propositions you have
already proved but were not in the initial knowledge base.

\(Z\)

\(\neg P\)

\(\neg (J \wedge Q)\)

\(\neg J\)

\(\neg T\)

Task 4 (25 pts)

Rewrite the following statements in first-order logic, stating
definitions for the predicates you use. (Note, one of these is
exceedingly hard, yet still possible; make an attempt…)